Excess Properties
2001. 2. 16Kwon Jung Hun
Thermodynamics and properties
ContentsI. Behavior of Excess Properties of Liquid Mixtures
1. Excess Gibbs energyExcess enthalpy • • • • relationsExcess entropy
2. Definitions of Regions on the vs. Diagram
II. Wohl’s Expansion for the Excess Gibbs Energyvan Laar Equation, Margules Equation …
III. Wilson, NRTL, and UNIQUAC Equations
ĝ ĥ
Thermodynamics and properties
I. Behavior of Excess Properties 1. Excess Gibbs energy, Excess enthalpy, Excess
entropy are related by
EEE Tshg −=
Rs
RTh
RTg EEE −=
XP
EE
TRTgT
RTh
,
)/(
∂
∂−=
Thermodynamics and properties
Definitions of Regions on the vs. Diagram
For convenience,
at
• 액체혼합물의 과잉물성과 상대적 크기들은 공학적목적이나 관찰된 용액의 거동을 근거로 분자현상을규명하는데 유용하게 쓰인다.
ĝ ĥ
Rcc
RssRThh
RTgg
EP
E
E
E
/ˆ
/ˆ/ˆ/ˆ
≡
≡≡
≡
5.021 == xx
Thermodynamics and properties
Definitions of Regions(I~VI) Definitions of Regions on the vs. Diagramĝ ĥ
Thermodynamics and properties
50°C 의 6성분계과잉물성(a) 클로로포름(1)/n-헵탄(2) (b) 아세톤(1)/메탄올(2)(c) 아세톤(1)/ 클로로포름(1) (d) 에탄올(1)/ n-헵탄(2) (e) 에탄올(1)/ 클로로포름(2) (f) 에탄올(1)/ 물(2)
Thermodynamics and properties
Trends for equimolar mixtures( 298K의 2성분계 )
[그림설명]
: NP/NP 혼합물: NA/NP 혼합물: AS/NP 혼합물: AS/NA 혼합물과
AS/AS 혼합물: 용매화 NA/NA
혼합물
Thermodynamics and properties
II. Wohl’s Expansion for the Excess Gibbs Energy
Wohl’s Expansion
van Laar Equation
22
211122
32112222
311112
221122
22
111221122211
6443
32)(
zzazzazzazza
zzazzaqxqxRT
g E
++++
+=+
2211
222
2211
111 , qxqx
qxzqxqx
qxz+
=+
=
2211
2121122qxqxqqxxa
RTgE
+=
Thermodynamics and properties
Wohl’s Expansion
Margules Equation
Scatchard-Hamer Equation
41
31
22
42
32
221
')'38'()'2'
23'(ln
'''ln
xCxCBxCBA
xCxBxA
++−++=
++=
γ
γ
31
1
221
1
22
32
221
)('))('23'(ln
''ln
zvvBz
vvBA
zBzA
−+=
+=
γ
γ
Thermodynamics and properties
III. Wilson, NRTL,and UNIQUAC Equations
(1) Wilson Equation* 개념 … 각 성분 분자 주위의 국부적 환경이 용액
내의 거시적인 몰용액의 특성과 다름
* 완전 혼합 용액에서 적용 가능
)ln()ln( 1212221211 xxxxxxRTg E Λ+−Λ+−=
)()ln(ln1212
21
2121
12221211 xxxx
xxxΛ+
Λ−Λ+
Λ+Λ+−=γ
)()ln(ln1212
21
2121
12112122 xxxx
xxxΛ+
Λ−Λ+
Λ−Λ+−=γ
)exp( 11121
212 RT
λλυυ −−=Λ )exp( 2221
12
121 RT
λλυυ −−=Λ
Thermodynamics and properties
(2) NRTL Equation
* 완전한 혼합 성계와 불완전한 혼합의 적용
)(1212
1212
2121
212121 Gxx
GGxx
GxxRTg E
++
+= ττ
RTgg 1121
21−=τ
RTgg 2212
12−=τ
)exp( 211221 τα−=G)exp( 121212 τα−=G
))(
)((ln 21212
12122
2121
2121
221 Gxx
GGxx
Gx+
++
= ττγ
))(
)((ln 22121
21212
1212
1212
212 Gxx
GGxx
Gx+
++
= ττγ
Thermodynamics and properties
Wilson Equation과 NRTL Equation의비교[ system : ethanol(1) / water(2) ]
Thermodynamics and properties
Wilson Equation과 NRTL Equation의비교
Thermodynamics and properties
Wilson Equation과 NRTL Equation의비교
Excess property
-800.00
-600.00
-400.00
-200.00
0.00
200.00
400.00
600.00
800.00
1000.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
x1
GE
HE
TSE
Thermodynamics and properties
Wilson Equation과 NRTL Equation의비교
energy change of mixing
-1200.00
-1000.00
-800.00
-600.00
-400.00
-200.00
0.00
200.00
400.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
delta H
delta G
delta S
Thermodynamics and properties
(3) UNIQUAC Equation
* 극성 , 무극성 , partial miscible mixture에서도 적용* 단지 2개의 ajustable parameter만으로도 대부분의경우에 잘 만족시킴
residual
E
ialcombinator
EE
RTg
RTg
RTg
+
=
Φ
+Φ
+Φ+Φ=
*2
222*
1
111
2
*2
21
*1
1 lnln2lnln θθ qxqxz
xx
xx
RTg
ialcombinator
E
)ln()ln( 12'
1'2
'2221
'2
'1
'11 τθθτθθ +−+−=
qxqx
RTg
residual
E
Thermodynamics and properties
[ The definitions of parameters ]
2211
22*2 rxrx
rx+
=Φ2211
11*1 rxrx
rx+
=Φ
2211
222 qxqx
qx+
=θ221111
1 qxqxqx
+=θ
'22
'11
'11'
1 qxqxqx
+=θ '
22'11
'22'
2 qxqxqx
+=θ
)exp()exp( 121212 Ta
RTu −≡Δ−=τ )exp()exp( 212121 T
aRTu −≡Δ−=τ
Thermodynamics and properties
UNIQUAC Equation
+
−+
++−
−Φ+
Φ+Φ=
12'
1'2
12
21'2
'1
21'1
'221
'2
'1
'12
2
11
*2*
1
11
1
*1
1 )ln(ln2lnln
τθθτ
τθθτθτθθθγ qql
rrlqz
x
+
−+
++−
−Φ+
Φ+Φ=
21'2
'1
21
12'
1'2
12'2
'112
'1
'2
'21
1
22
*2*
2
22
2
*2
2 )ln(ln2lnln
τθθτ
τθθτθτθθθγ qql
rrlqz
x
)1()(2 1111
−−−= rqrzl )1()(2 2222
−−−= rqrzl
[ Merits of UNIQUAC Equation ] ... (relative) simplicity
only two ajustable parameter
wide range of applicability
Thermodynamics and properties
[참고] Activity models